WitnessComplex: R6 Class for Witness Complex

In rgudhi: An Interface to the GUDHI Library for Topological Data Analysis

R6 Class for Witness Complex

Description

A Witness complex \mathrm{Wit}(W,L) is a simplicial complex defined on two sets of points in R^D. The data structure is described in \insertCiteboissonnat2014simplex;textualrgudhi.

Details

The class constructs a (weak) witness complex for a given table of nearest landmarks with respect to witnesses.

References

\insertCited

Super class

rgudhi::PythonClass -> WitnessComplex

Methods

Public methods

• WitnessComplex$new()

• WitnessComplex$create_simplex_tree()

• WitnessComplex$clone()

Inherited methods

• rgudhi::PythonClass$get_python_class()
• rgudhi::PythonClass$set_python_class()

---

Method new()

The WitnessComplex constructor.

Usage

WitnessComplex$new(nearest_landmark_table)

Arguments

nearest_landmark_table

A list of tibble::tibbles specifying for each witness w, the ordered list of nearest landmarks with id in column nearest_landmark and distance to w in column distance.

Returns

A WitnessComplex object storing the Witness complex.

---

Method create_simplex_tree()

Usage

WitnessComplex$create_simplex_tree(max_alpha_square = Inf)

Arguments

max_alpha_square

The maximum relaxation parameter. Defaults to Inf.

Returns

A SimplexTree object storing the computed simplex tree created from the Delaunay triangulation.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

WitnessComplex$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Author(s)

Siargey Kachanovich

See Also

Other filtrations and reconstructions: AlphaComplex, RipsComplex, TangentialComplex

Examples

withr::with_seed(1234, {
  l <- list(
    tibble::tibble(
      nearest_landmark = sample.int(10),
      distance = sort(rexp(10))
    ),
    tibble::tibble(
      nearest_landmark = sample.int(10),
      distance = sort(rexp(10))
    )
  )
})
wc <- WitnessComplex$new(nearest_landmark_table = l)
wc


withr::with_seed(1234, {
  l <- list(
    tibble::tibble(
      nearest_landmark = sample.int(10),
      distance = sort(rexp(10))
    ),
    tibble::tibble(
      nearest_landmark = sample.int(10),
      distance = sort(rexp(10))
    )
  )
})
wc <- WitnessComplex$new(nearest_landmark_table = l)
st <- wc$create_simplex_tree()
st$num_vertices()

rgudhi documentation built on March 31, 2023, 11:38 p.m.